* LME/ShFE arb: http://tmsnrt.rs/2oQ5nm2
* China zinc premiums highest in nearly three years
* Lead down 7 pct since start of May (Recasts, updates prices, adds comment/detail; changes dateline)
LONDON, May 19 (Reuters) - Copper rose on Friday and looked set to close the week higher thanks to the dollar's weakening and receding worries over China's economy, while zinc surged about 1.5 percent amid stock draws.
Stockmarkets in top metals consumer China ended the week higher, snapping a five-week losing streak as soothing regulatory comments and the central bank's cash injection offset worries over tighter banking regulations and economic growth.
The dollar was on track to record its worst week since August, having given up almost all the gains made since Donald Trump, now surrounded by political worries, was elected U.S. president last year.
"Doubts on the China (growth) front have been fading for the past week but increasing on the U.S. front and that's constraining the upside," said Nitesh Shah, commodity strategist at ETF Securities.
"I see metals treading water for the next few weeks, but thereafter they are likely to increase (assuming) this negative sentiment from the U.S. fades. In a year of political change in China things aren't going to be allowed to fall off a cliff."
* PRICES: London Metal Exchange copper rose 0.7 percent to $5,619.50 a tonne by 1020 GMT. Prices were set for a small weekly gain of 0.8 percent. Leading base metal price gains, zinc was up 1.5 percent at $2,571 a tonne.
* GLOBAL MARKETS: World stocks headed for their first weekly fall in five as uproar over Trump's firing of former FBI director James Comey and his campaign's alleged ties with Russia prompted uncertainty about his ability to push through his economic policies any time soon.
* COPPER STOCKS: Copper stocks in warehouses monitored by the Shanghai Futures Exchange rose 0.7 percent from last Friday to 196,358 tonnes.
* CHINA ZINC: Premiums for zinc in China jumped by $10 to $155 a tonne, the highest in nearly three years, as the gap between local and global prices turned favourable for imports.
* CHINA ZINC: China is likely to step up imports of refined zinc from this month, industry sources said on Friday, as dwindling global supplies of concentrate hit local output of the metal, used to galvanise steel.
* ZINC STOCKS: LME data showed 28,925 tonnes of zinc were booked to leave exchange warehouses, sending 'on-warrant' or available stocks down to 170,200 tonnes, their lowest since October 2008. <MZN-STOCKS>. Zinc stocks in warehouses monitored by the Shanghai Futures Exchange fell 9.5 percent from last Friday to 91,749 tonnes.
* LME LEAD: has fallen 7 percent since the start of May due to rising supply with stocks in China surging above 80,000 tonnes to the highest since March 2014. <PB-STX-SGH> ($1 = 6.8915 Chinese yuan renminbi)
(Additional reporting by Melanie Burton; Editing by Susan Fenton)