In a pipette tip rack including a base and vertically extending side members, the combination of a horizontally extending pipette tip support tray over the base of the tip rack and a plurality of large maximized internal volume freely nestable pipette tips having an internal volume of 500 microliters or more, the support tray including a plurality of through holes arranged in an array, each hole having a center which is spaced a distance "s" from centers of immediately adjacent through holes, "s" being approximately 9 millimeters, each pipette tip having a substantially cylindrical proximal portion and an elongated generally conical distal portion coaxial with and joined to its proximal portion adjacent a downwardly facing outwardly extending shoulder and including at a distal tip end a relatively small orifice for receiving and dispensing fluid into and from the pipette tip upon operation of a pipette to which the pipette tip is mounted, the proximal portion of each pipette tip having an outer diameter equal to or approximately equal to but less than "s" and a conical inner surface for receiving and releasably attaching to a pipette tip mounting shaft of the pipette, the distal portion of each pipette tip being vertically oriented in a different one of the through holes in the support tray with its shoulder on a top of the support tray for support thereby to form a first array of pipette tips supported by the pipette tip rack, and the distal portion of each pipette tip further including substantially parallel inner and outer surfaces tapering inward in a downward direction relative to a vertical longitudinal axis of the pipette tip to maximize the inner volume of the central portion and for spacing from an outer surface of a similar pipette tip of a second array of pipette tips when nesting in the first array of pipette tips.