Bank-owned online broking businesses enjoyed a strong June half, with growth in customer numbers and market share.According to the latest Investment Trends online broking report, the number of active online share investors rose four per cent over the six month to June.During that period 620,000 unique Australian investors placed at least one trade with an online broker, compared with 595,000 during the six months to the end of last year and 585,000 in the June half last year.Investment Trends said Commonwealth Bank's CommSec service and National Australia Bank's nabtrade were the big movers in market share.CommSec increased its share by three percentage points to 44 per cent and nabtrade increased its share by two percentage points to ten per cent (share is measured as primary relationships).ANZ's E*Trade was steady at 14 per cent.Sixty per cent of online investors used a mobile device for share trading - up from 53 per cent a year ago."A good mobile platform is becoming a must-have asset when targeting first-time investors," said Investment Trends analyst Irene Guiamatsia.The survey also revealed growing demand for access to international shares on online share broking platforms.