* Hopes for easing from BOJ support market * China-related stocks extend gains * Google, Microsoft earnings hurt Yahoo Japan * NEC jumps after earnings overshoot guidance by a mile By Sophie Knight TOKYO, Oct 19 (Reuters) - Japan's Nikkei share average topped the 9,000 level on Friday to log its best weekly gain in nearly a year as expectations of easing from the Bank of Japan and robust risk sentiment on the back of an improved global outlook softened the yen for the seventh day. The benchmark also marked a fresh three-week high after a steep four-day rally, as an easier yen benefited exporters and China-related stocks climbed higher after data on Thursday suggested the country's slowdown is bottoming out. "The deceleration of China's economy seems to have dropped its pace, which is a supporting factor, but basically people are adjusting their positions before the BOJ meeting," said Hideyuki Ishiguro, senior strategist at Okasan Securities, referring to the Bank of Japan. At its next policy meeting on Oct. 30, the central bank will likely cut its growth forecasts and may debate expanding its asset-buying programme, to contain the effects of a global slowdown on the export-reliant economy, sources familiar with its thinking said. "The focus is now not on whether they will ease or not, but rather what kind of easing they will do. They understand that if they don't put out something impressive enough to convince the markets it will hurt the economy," Ishiguro said. The Nikkei inched up 0.2 percent to 9002.68, logging a gain of 5.5 percent since last Friday's close that marked its best weekly performance since early December 2011. The benchmark made several tentative forays into negative territory through the day, however, as some investors took poor earnings from U.S. tech firms to take profits on cyclicals that saw big gains this week. Yahoo Japan slipped 2.3 percent after Google's third-quarter earnings and revenue came in well under forecasts as its core advertising business slowed, sending its shares down 8 percent, while Microsoft's quarterly profit fell more than expected, hurt by the industry-wide slump in PC sales. However, earnings in the U.S. have overall been stronger than expected, leading investors to judge last week's aggressive sell-off as overdone and to buy back some battered stocks. NEC Corp bounced back 10.5 percent following a drop of 4.6 p ercent on Thursday, after the company surprised investors by raising its guidance for the period to 47 billion yen ($593 million) from a previous forecast of 1 billion yen, after restructuring boosted profit margins. The broader Topix index added 0.3 percent to 754.39 in strong trade, with 1.75 billion shares trading hands, although it had ebbed from Thursday's 2.01 billion, the highest volume in a month. TIME TO REIN BACK OPTIMISM? Optimism that China's slowdown might have bottomed out helped industrial robotics maker Fanuc Ltd, which has large exposure to the country, gain 3.9 percent, lending 20 positive points to the benchmark. Similarly, machinery construction maker Komatsu Ltd , often used as a barometer for sentiment towards China, was just behind Fanuc as the third-most traded stock on the main board, moving up 2.8 percent. Komatsu's gains helped the machinery subindex to be the best-performing sector, with air-conditioner maker Daikin Industries Ltd also rising 4.2 on a softer yen and news it will release a dehumidification system for factories that consumes 60 percent less electricity. However, there were some doubts that the Nikkei would be able to hang onto the week's gains as the earnings season moves into higher gear from next week, with the majority of firms expected to lower their outlook for the rest of the year. For some, increased optimism surrounding China, Japan's biggest export market, is overdone, considering there is little sign of the economy picking back up and boycotts of Japanese products on the back of a territorial dispute continue. "It's not as if the problems with China have gone away or been fully priced in, people have just forgotten about them, as with the euro zone," said Makoto Kikuchi, CEO OF Myojo Asset Management. A Bank of America Merrill Lynch report said that 38 percent of investors are now underweight on Japanese stocks, 15 percent more than in September, while 20 percent deemed the country's equity market unfavorable because of expected weakness in corporate earnings, 6 more than last month.